I wouldn't use "propaganda." You could say "minister of public affairs" or "minister of the publicity/communications department"

First off, propaganda has very negative connotations. You only want to use that word if you're talking about an authoritarian government intentionally manipulating people. Publicity is the positive term for representing a brand, person or organization. Next, the word "Minister" in an organizational context is very British. In the US federal government, the top officials are usually called "Secretaries," such as the Secretary of State. In student organizations, it's more common to say "Officer," such as Public Affairs Officer. That said, if you're going to use the word "Minister," I'd recommend Minister of Public Affairs as Emilia suggested above.

"propaganda" has a bad connotation (it usually implies political maneuvering). "publicity" is better but I think it's more about creating news and grabbing attention than having good relations with the public. What you mentioned is usually called "public relations", often abbreviated as PR. This is a neutral term in common use. It sounds a little big for a student union, but I think it's okay to use.